Physically based shading with area light is a challenging topic in computer graphics. Namely, a point light source modeling for approximating the lighting has generally been exploited in CGI and video games, due to its mathematical simplicity. However, it suffers from severe limitations when located close to surfaces. Area lights provide more natural lighting, giving notably VFX (visual effects) and game creators finer control on light balancing within a scene, to reduce contrast or match some artistic criteria.
In what follows, the term “rendering” refers broadly to the conversion of geometry and material data into visual images.
Also, the word “glossy” generally refers to shininess, and can pertain to specular reflection as well as transmission. Typically, smooth surfaces appear shiny or glossy to the eye, due to a significant amount of light being focused around a privileged direction.
In this respect, a glossy surface in reflection is nearly-specular. Namely, while a perfectly smooth surface obeys Snell's law, which involves a unique reflection direction for any incoming ray (that direction being symmetric with respect to the incoming ray with respect to a normal to the illuminated surface), more realistic representations rely on reflected light distribution around that direction. The latter constitutes then merely a preferred direction for reflected light.
More generally, a radiation reflected by a surface is usually represented as comprising a glossy part, identified as a specular component, in addition to diffusion and/or ambient parts, respectively representative of an ambient lighting reflection and a diffuse reflection by the illuminated surface.
Similarly, a glossy surface in transmission (or a glossy part of a transmitted radiation) involves a light distribution around the Snell law direction of transmission—corresponding to transparency. A glossy object in transmission appears then typically as “frosted glass”.
In what follows, a glossy radiation, or a glossy part of a radiation, designates a radiation concentrated around an oriented axis, whether in reflection or in transmission. In a more specific kind of glossy radiation, the behavior of the radiation around that axis is controlled by a cosine function raised by a n-power. The n power is then a glossiness or shininess constant coefficient that is worth at least 1, and is typically worth several tens or hundreds. The larger n, the more the glossy reflection is close to a perfect mirror-like specularity (smaller and sharper highlights), or the glossy transmission is close to a perfect transparency transmission. The cosine is further given by the angle between the oriented axis and a viewing direction.
Considering reflection, widespread models for the specular term are based on Phong lighting, which provides an empirical representation of local illumination of points on a surface, as well known to a person skilled in the art. Accordingly, the specular component of light reflected at a surface reflection point contains a factor derived from the dot product of a unit vector {right arrow over (γ)} corresponding to the mathematical reflection of the viewing direction over the surface at the considered reflection point, and of a unit vector {right arrow over (ω)}i (“i” standing for incoming) pointing to the light source. That factor is then given by the dot product raised by an n-power, where n stands for a Phong exponent, which corresponds to the shininess constant above:({right arrow over (ωi)}·{right arrow over (r)})n,Computing such an n-power factor proves generally computationally expensive, notably compared with the calculation of the diffuse and ambient terms. This is especially true with an area light source, because computations must be iterated over the surface of the light source.
Similar demanding computations are required for rendering an object that is glossy for light transmission, or for which part of the transmission is modelled as glossy.
As a whole, existing techniques for processing area light sources either require huge computation time to achieve good results or make some quality trade-off to work in real time.
In order to estimate the radiance of glossy surfaces illuminated by area lights (the radiance designating a light flux density per unit solid angle per unit area), two families of approaches have been developed: sampling ones and analytic ones.
The sampling approaches rely on discrete evaluation of the radiance integral either by considering discretization area light surface or by considering a stochastic sampling (typically Monte Carlo integration) of the hemisphere surrounding a receiving point. While those techniques work quite well with Lambertian surfaces, they require a huge amount of samples when dealing with non Lambertian surfaces, resulting in high computational costs.
Analytical approaches have been developed in particular by James Arvo, in his PhD thesis “Analytic methods for simulated light transport”, Yale University, 1995, and in his article “Applications of Irradiance Tensors to the Simulation of Non-Lambertian Phenomena”, In Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, 1995. He introduced a closed form expression of radiance integral based on tensor theory and Stokes theorem, for polygonal light sources and Phong reflectance models. The surface integral is developed as a sum of 1D line integrals for which an analytic though complicated expression exists. Using integration by parts, a recurrence relation is derived, allowing incremental evaluation of the line integrals in
  O  ⁡      (                  n        +        2            2        )  time.
The solution can be easily implemented in a GPU using any shading or computing language for real-time performances. However, for surface with high-order Phong exponents (e.g. greater than 100), the evaluation becomes computationally expensive. To overcome that issue, Arvo proposes early termination of the iteration loop once a desired relative accuracy is reached. Anyway, in many situations, the number of iterations is high for reaching performance hits during navigation. Moreover, execution of variable length on a GPU may result in poor performances due to code path divergence on parallel threads.